1. Multicarrier Modulations
1.1 OFDM Modulations
To date, there are known OFDM (orthogonal frequency division multiplex) type multicarrier modulations. Such a modulation technique provides an efficient solution to the broadcasting of information, especially for radio or wired type multiple-path channels.
The OFDM multicarrier modulation technique has therefore been chosen in several standards and specifications for wire transmission applications, for example of the ADSL (asymmetric digital subscriber line) and PLC (power line communication) type or wireless applications for example of the DAB (digital audio broadcasting), DVB-T (digital video broadcasting-terrestrial) and WLAN (wireless local area network) types.
However, the rectangular shaping of a signal as performed by an OFDM modulator has the drawback of poor frequency location.
Consequently, alternative solutions have been proposed, leading to multicarrier modulation systems in which the signal is shaped by functions known as prototype functions which give better frequency location.
It may be recalled that the set of sub-carriers of a multicarrier modulation forms a multiplex and that each of the sub-carriers of this multiplex can be shaped by means of a same prototype function denoted g(t) which characterizes the multicarrier modulation.
1.2 OFDM/OQAM Modulations
Thus, one proposed solution entails replacing a QAM (quadrature amplitude modulation) implemented by each of the sub-carriers by a modulation which offsets the real and imaginary paths of the complex data to be transmitted, for two successive carrier frequencies, by a half symbol period.
This alternation leads to an OFDM/OQAM type multicarrier modulation. This approach makes it possible especially to achieve requisite conditions of orthogonality with prototype filters which are not necessarily rectangular. Indeed, the temporal offset introduced by the OQAM modulation loosens the constraints of orthogonality or more generally the conditions of bi-orthogonality. This class of modulation thus provides a wider choice of prototype functions than that given by the simple rectangular prototype function of an OFDM modulation.
Thus, depending on the type of transmission channel considered for a given application, such as for example the radiomobile channel or the power line carrier (PLC) channel, it is possible to make a choice of prototype functions suited to the type of specifications and/or distortions encountered. In particular, it is preferable to choose prototype functions having better frequency selectivity than the cardinal sine function used in OFDM modulation, especially in radiomobile channels, to combat the frequency dispersion due to the Doppler effect or again in PLC applications to better withstand narrow-band scramblers and, generally speaking, to meet the frequency specifications of the transmission masks more easily.
More specifically, the OQAM signal can be represented in baseband in the following form:
                              s          ⁡                      (            t            )                          =                              ∑            n                    ⁢                                          ⁢                                    ∑                              m                =                0                                            M                -                1                                      ⁢                                                  ⁢                                          a                                  m                  ,                  n                                            ⁢                                                                                          g                      ⁡                                              (                                                  t                          -                                                      n                            ⁢                                                                                                                  ⁢                                                          τ                              0                                                                                                      )                                                              ⁢                                          ⅇ                                                                                                    j2π                            ⁢                            mv                                                    0                                                ⁢                        t                                                              ⁢                                          ⅇ                                              jϕ                                                  m                          ,                          n                                                                                                      ︸                                                                      g                                          m                      ,                      n                                                        ⁡                                      (                    t                    )                                                                                                          (        1        )            
with:                am,n the real-value data symbols to be transmitted on a sub-carrier m at the instant n;        M the number of carrier frequencies (necessarily an even-parity value);        g the prototype function used by the modulator;        τ0 the duration of a multicarrier symbol;        v0 the spacing between two adjacent sub-carriers of the multiplex;        φm,n a phase term chosen so as to achieve a real-part/imaginary-part alternation enabling orthogonality or more generally bi-orthogonality.        
The OFDM/OQAM modulation is therefore an alternative to the classic OFDM modulation relying on a judicious choice of the prototype function modulating each of the sub-carriers of the signal which must be properly located in the time/frequency space.
It may be recalled that the OFDM type modulations classically transmit complex-value data symbols while the OFDM/OQAM type modulations transmit real-value data symbols, an OFDM/QAM complex-value data symbol or an OFDM/OQAM real-value data symbol being constituted by a set of data elements at a given instant t.
The spectral efficiency of the OFDM/OQAM is therefore identical to that of classic OFDM without any guard interval. Indeed, for a same inter-carrier spacing v0, there is transmitted:                in OFDM/OQAM modulation, one real value per sub-carrier every time slot τ0;        in classic OFDM modulation without guard interval, one complex value (i.e. two real values) every 2×τ0.        
If we consider an OFDM type modulation with a guard interval, where a symbol with a duration 2τ0 is extended by a guard interval with a duration Δ, the spectral efficiency of OFDM/OQAM is (Δ+2τ0)/2τ0 times greater than that of the OFDM type modulation.
It may also be recalled that the OFDM/OQAM type modulation techniques do not require the introduction of a guard interval or a cyclic prefix while at the same time presenting the same spectral efficiency as classic OFDM modulations.
1.3 BFDM/OQAM Modulation
In addition, if it is chosen to have demodulation functions on the reception side that are not necessarily the functions conjugate to the prototype functions used in transmission, then it is possible, in using the property of bi-orthogonality, to extend the use of OFDM/OQAM to the technique of BFDM/OQAM modulation. Indeed, the offset principle related to the OQAM family is strictly identical in BFDM/OQAM type modulation.
More specifically, the usefulness of the BFDM/OQAM type modulation is that, for a given length of prototype filter, it reduces the delay given by the transmission system.
As indicated here above, the BFDM/OQAM type modulation technique, just like the OFDM/OQAM modulation technique, transmits real-value data symbols at a rate twice that at which the OFDM type modulation transmits complex-value data symbols. Consequently, these two modulations have the same spectral efficiency in principle.
Indeed, in the bi-orthogonal case, the demodulation base at reception can be different from that at transmission and can be expressed in the following form:fm,n(t)=f(t−nτ0)ej2πmv0tejφm,n  (2)
The condition of bi-orthogonality can then be expressed in the following form:
                                          〈                                          g                                  m                  ,                  n                                            ,                              f                                                      m                    ′                                    ,                                      n                    ′                                                                        〉                    R                =                                          ⁢                          {                                                ∫                                      -                    ∞                                    ∞                                ⁢                                                                            g                                              m                        ,                        n                                                              ⁡                                          (                      t                      )                                                        ⁢                                                            f                                                                        m                          ′                                                ,                                                  n                          ′                                                                    *                                        ⁡                                          (                      t                      )                                                        ⁢                                                                          ⁢                                      ⅆ                    t                                                              }                                =                                    δ                              m                ,                                  m                  ′                                                      ⁢                          δ                              n                ,                                  n                  ′                                                                                        (        3        )            
where: .,.R designates the real scalar product and {.} designates the real part.
Here below, we use the acronym OQAM to designate both OFDM/OQAM techniques and BFDM/OQAM type techniques.
1.4 MC-CDMA Modulations
In applications where spectral resources have to be shared between several users, also called subscribing users, within a transmission band, the OFDM modulation known as the classic modulation (with guard interval and achieved by simple fast Fourier transform) can be associated with a CDMA (code division multiple access) type multiple access technique.
This technique, also called MC-CDMA, has been extensively studied in the radiomobile context and is also envisaged for PLC applications.
More specifically, it enables a set of users to make simultaneous transmission in a same frequency band.
CDMA type multiple access is considered in various systems because of its flexibility in terms of access and its performance obtained in cell networks using a unit frequency re-utilization factor. Such a technique provides flexibility to the new systems of mobile and cell communications which must be capable of providing both fast transfer of data for a reduced number of users as well as a less rapid but robust transfer for data for a very large number of users in uplink and downlink modes.
The MC-CDMA technique is chiefly studied in the communications downlink (synchronous links) and enables different users to occupy the same time-frequency space by distinguishing each user with a spreading code which is the user's own code.
The codes associated with each user, also called spread-spectrum codes, are orthogonal and are for example derived from a Walsh-Hadamard type matrix.
For the downlink, each mobile terminal of the communications system processes only one transmission channel restoring the orthogonality of the codes in reception by a simple equalization of the signal of the “zero forcing” (ZF) or minimum mean squared error (MMSE) type.
However, on the uplink, the propagation of the data stream coming from the various users through the different propagation channels prompts a great loss of orthogonality of the spread-spectrum codes which cannot be totally restored, thus giving rise to high multiple-access interference (MAI). MAI then leads to mediocre performance in transmission if an equalization identical to that of the downlink is achieved. On the uplink, the MC-CDMA technique therefore makes it necessary to implement detectors of greater complexity.
MC-CDMA modulation achieves a spread-spectrum of the stream of data on different sub-carriers. The spread-spectrum sequence is thus applied in the frequency domain, thus allowing to benefit from the frequency diversity of the channel.
In addition, the advantage of applying a spread-spectrum in the frequency domain is that it is possible in reception to retrieve all the dissipated energy of the signal and use it to render the transmitted signal in the most efficient way possible.
More specifically, referring to FIG. 1, we present the generally structure of a MC-CDMA transmission system for a user j.
After a series/parallel conversion (not shown in the figure), each complex-value data symbol dn,u,0(c), dn,u,1(c), . . . , dn,u,N0−1(c) undergoes Nc replicas where dn,j,m(c) represents the mth complex-value data symbol of the jth user at the instant n, and Nc is the length of the spreading codes. Thus, the same data symbol is transmitted on Nc different sub-carriers.
Let us consider for example the data symbol dn,u,0(c): each replica 111, 112, . . . , 11Nc of the data symbol has a spread chip proper to each user applied to it.
For example, the chip c0,u of the spreading code associated with the user u is applied to the first replica 111 of the data symbol dn,u,0(c), the chip c1,u is applied to the second replica 112 of the data symbol dn,u,0(c), and the chip cNc−1,u is applied to the last replica 11Nc of the data symbol dn,u,0(c).
It can be noted especially that, should the number of modulated sub-carriers Npm be equal to the size of the code Nc, the series/parallel conversion is not done.
The symbols coming from the spreading operation then undergo a classic OFDM type multicarrier modulation 12 (reverse Fourier transform followed by an insertion of a guard interval).
It is then deemed to be the case that each sub-carrier of the MC-CDMA signal conveys a part of the symbol corresponding to a chip of the spreading code, thus introducing frequency diversity.
The MC-CDMA technique therefore has two fields of orthogonality: that of the frequencies for the data of a same user and that of the spreading codes between users.
One of the main uses of this technique lies in the flexibility of allocating spectral resources and hence of the bit rate of information transmitted. Indeed, if a user needs to transmit at an information bit rate greater than a basic bit rate (it may be recalled that a spreading code has a corresponding given bit rate), the network will, as far as possible, assign it different spreading codes sequences, of course to the detriment of a reduction in the number of simultaneous users.
Should the U users each use a single code to transmit their data, the expression of the signal sent is:
                                          s            ⁡                          (              t              )                                =                                    ∑              n                        ⁢                                                  ⁢                                          ∑                                  m                  =                  0                                                                      N                    0                                    -                  1                                            ⁢                                                          ⁢                                                ∑                                      p                    =                    0                                                                              N                      o                                        -                    1                                                  ⁢                                                                  ⁢                                                      ∑                                          j                      =                      0                                                              U                      -                      1                                                        ⁢                                                                          ⁢                                                            d                                              n                        ,                        j                        ,                        m                                                                    (                        c                        )                                                              ⁢                                          c                                              p                        ,                        j                                                              ⁢                                          ⅇ                                              2                        ⁢                        ⅈ                        ⁢                                                                                                  ⁢                        π                        ⁢                                                                                                  ⁢                                                  F                                                                                    mN                                                              o                                +                                p                                                                                      ⁢                            t                                                                                                                ⁢                                          g                      ⁡                                              (                                                  t                          -                                                      nT                            s                                                                          )                                                                                                                                ⁢                                  ⁢                  with          ⁢                      :                          ⁢                                  ⁢                                            F                                                mN                  o                                +                p                                      =                                          F                0                            +                                                                    mN                    o                                    +                  p                                                  2                  ⁢                                      τ                    0                                                                                ;                                    (        4        )                            Ts=2τ0+Δ;        N0 being the number of pieces of data transmitted in a multicarrier symbol per user such that        
            N      0        =                  number        ⁢                                  ⁢        of        ⁢                                  ⁢        modulated        ⁢                                  ⁢        carriers                    N        c              ;                U being the number of simultaneous users;        
      c          p      ,      j        =            ±              1                              N            c                                ⁢                  ⁢    the    ⁢                  ⁢          p      th                       power-standardized chip of the spreading code of the user j;        the spacing between sub-carriers is equal to        
  1      2    ⁢          τ      0                       if 2τ0 is the useful duration of a multicarrier symbol.        
The MC-CDMA signal is then conveyed in the propagation channel 13 and demodulated and equalized in the block 14 (OFDM demodulation and equalization with elimination of the guard interval).
De-spreading corresponding to an operation which is appreciably the reverse of spreading is then implemented, delivering an estimation of complex data symbols.
This MC-CDMA transmission technique however has drawbacks linked to the use of an OFDM type multicarrier modulation.
Indeed, as already indicated, the OFDM modulation implies a loss of spectral efficiency due to the insertion of a guard interval.
Moreover, the gate function used in OFDM (for the rectangular shaping of the signal) is not properly located in frequency, thus making it sensitive to all the frequency drifts and entailing penalties with respect to transmission masks.
Besides, it must be noted that this transmission technique calls for the use of all the codes of a matrix of spreading codes (i.e. a full matrix of spreading codes) to attain the maximum bit rate of the system. We therefore use all the codes associated with this spreading matrix to attain the maximum capacity of the system.
1.5 OQAM-CDMA Real-Value Modulations
The use of an OQAM type modulation makes it possible especially to overcome the need for using a guard interval.
Thus, it has also been proposed to combine CDMA type multiple access techniques with OQAM modulation in which the data symbols transmitted are real-value symbols.
However, this transmission technique also calls for the use of a full matrix of spreading codes to attain the maximum bit rate of the system.